Transductive Bounds for the Multi-Class Majority Vote Classifier

In this paper, we propose a transductive bound over the risk of the majority vote classifier learned with partially labeled data for the multi-class classification. The bound is obtained by considering the class confusion matrix as an error indicator and it involves the margin distribution of the classifier over each class and a bound over the risk of the associated Gibbs classifier. When this latter bound is tight and, the errors of the majority vote classifier per class are concentrated on a low margin zone; we prove that the bound over the Bayes classifier' risk is tight. As an application, we extend the self-learning algorithm to the multi-class case. The algorithm iteratively assigns pseudo-labels to a subset of unlabeled training examples that have their associated class margin above a threshold obtained from the proposed transductive bound. Empirical results on different data sets show the effectiveness of our approach compared to the same algorithm where the threshold is fixed manually, to the extension of TSVM to multi-class classification and to a graph-based semi-supervised algorithm.